Question

If 5 men can build a wall in 12 days, how many days will 10 men take?

• A. 24
• B. 6
• C. 5
• D. 10

Hint:

Double the men, half the time!

Answer 1

The Correct Option is B

Step 1: Understand the Concept
This problem is based on the principle of Time and Work, specifically involving Inverse Proportion. In such scenarios, the number of men working is inversely proportional to the time taken to complete the work (assuming the total work remains constant). This means that if you increase the number of workers, the time required to finish the task will decrease.

Step 2: Analysis & Application
We use the work-equivalence formula: $M_1 \times D_1 = M_2 \times D_2$, where $M$ represents the number of men and $D$ represents the number of days.
From the question, we have the initial data:
$M_1 = 5 \text{ men}$ and $D_1 = 12 \text{ days}$.
The new condition is:
$M_2 = 10 \text{ men}$ and we need to find $D_2$.
Substituting these values into the formula:
$5 \times 12 = 10 \times D_2$.

Step 3: Calculation & Conclusion
First, calculate the total "man-days" required for the project:
$60 = 10 \times D_2$.
Now, solve for $D_2$ by dividing both sides by 10:
$D_2 = \frac{60}{10} = 6$.
Therefore, with the workforce doubled, the time taken to build the wall is halved, resulting in 6 days.

Final Answer: (B)